Why is the movie titled "Her" instead of "She"?

A possible explanation:

Theodore falls deeply in love with Samantha, and she with him, but she is a mystery, a mystery partly signalled by the title: "her" rather than "she", the object of a man's perception and entranced bafflement.

Another:

The title of Her, Spike Jonze’s excellent but deceptively dark new film, is less anodyne than it first appears: the antecedent of that pronoun is properly not a her but an it. “Her” is Samantha, or rather “Samantha”—a computer/smartphone operating system, voiced by Scarlett Johansson in her signature New York contralto, developed some time in the near future and purchased by Theodore (a finely withdrawn Joaquin Phoenix), who soon falls in love with her.

[...] “It’s not just an OS. It’s a consciousness”—so goes the tagline for OS1, and note the pronoun choice.

[...] Instead Jonze skips directly to Theodore booting up the new OS, which, in Johansson’s voice, identifies herself (I feel manipulated using that word, but itself seems impossible) as Samantha. [...]

[...] As Theodore begins to use the OS nonstop, even sleeping with it — less creepy when that it feels like a her — not just his data but his entire life become a form of economic production for an unseen company. [...]

[...] Samantha, or the thing we call Samantha, does not enslave Theodore; but Element Software does, via the deception that such a being as “Samantha” exists, that it is in fact a her. [...]

One reason to avoid "She" as a title would be to avoid confusion with the many film adaptations of H. Rider Haggard's She: https://en.wikipedia.org/wiki/She:_A_History_of_Adventure#Adaptations

"She" is the subjective pronoun, while "her" is the objective pronoun. So the choice of "her" indicates that the title character is the object, rather than the performer, of the action, as Theodore, not Samantha, is the primary viewpoint character.